Practice Flashcard 3.1-3.2 Ac Pre calc

Front

What is the formula for compound interest?

Back

A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount (the initial amount of money), r is the annual interest rate (decimal), n is the number of times that interest is compounded per year, and t is the number of years the money is invested or borrowed.

Front

What does it mean for two functions to be inverses?

Back

Two functions are inverses if the output of one function becomes the input of the other, and vice versa. For example, if f(x) = y, then f^(-1)(y) = x.

Tags

CCSS.HSF-BF.B.4B

Front

How do you convert a logarithmic equation to an exponential form?

Back

To convert log_b(a) = c to exponential form, rewrite it as b^c = a.

Tags

CCSS.HSF.BF.B.5

Front

What is the relationship between exponential functions and logarithmic functions?

Back

Exponential functions and logarithmic functions are inverses of each other.

Tags

CCSS.HSF.BF.B.5

Front

What is the natural logarithm?

Back

The natural logarithm, denoted as ln(x), is the logarithm to the base e, where e is approximately equal to 2.71828.

Front

How do you express e^x in logarithmic form?

Back

The expression e^x = y can be rewritten in logarithmic form as ln(y) = x.

Tags

CCSS.HSF.BF.B.5

Front

What is the effect of a positive constant added to a function's output?

Back

Adding a positive constant to a function's output shifts the graph of the function upward.

Front

What is the effect of a negative constant added to a function's input?

Back

Adding a negative constant to a function's input shifts the graph of the function to the left.

Front

What is the formula for the total return on an investment with compound interest?

Back

Total return = Principal * (1 + interest rate)^(number of years).

Front

How do you find the total amount after 3 years for an investment of $20,000 at 5.2% interest compounded annually?

Back

Total amount = 20000 * (1 + 0.052)^3 = $23,285.05.